AP CALCULUS BC TIMELINE
This subpage outlines the Unit Topics that will be covered throughout the course. In addition, the concept notes, homework and homework answers from each Unit have been posted for your review throughout the academic school year. Position the mouse over Unit Concept Notes and click on the desired unit to see the unit's information.
FALL SEMESTER - AB TOPICS
Unit 1 Limits, Continuity & Derivative Concepts 2 Weeks – August
1.1 Limit of a Function Two Sided, One Sided, & Infinite Limits
1.2 Calculating Limits with limits of absolute value functions and squeeze theorem
1.3 Limits at Infinity
1.4 Squeeze Theorem
1.5 Continuity Two-sided & One-sided Continuities, Intermediate Value Theorem
1.6 Estimate Tangent Lines
1.7 Calculating Tangent Lines
1.8 Derivative of a Function
1.9 Differentiability
1.1 Limit of a Function Two Sided, One Sided, & Infinite Limits
1.2 Calculating Limits with limits of absolute value functions and squeeze theorem
1.3 Limits at Infinity
1.4 Squeeze Theorem
1.5 Continuity Two-sided & One-sided Continuities, Intermediate Value Theorem
1.6 Estimate Tangent Lines
1.7 Calculating Tangent Lines
1.8 Derivative of a Function
1.9 Differentiability
Unit 2 Differentiation Rules & Techniques 3.5 weeks – Ending August/Beginning September
2.1 Basic Differentiation Formulas Power Functions (including interpretation of velocity/acceleration – higher order derivatives)
2.2 Product Rule
2.3 Quotient Rule
2.4 Derivative Applications
2.5 Derivatives of Trigonometric Functions
2.6 Chain Rule
2.7 Implicit Differentiation
2.8 Derivatives of Exponential Functions
2.9 Derivatives of Logarithmic Functions
2.10 Logarithmic Differentiation
2.11 Derivatives of Inverse Trig Functions
2.1 Basic Differentiation Formulas Power Functions (including interpretation of velocity/acceleration – higher order derivatives)
2.2 Product Rule
2.3 Quotient Rule
2.4 Derivative Applications
2.5 Derivatives of Trigonometric Functions
2.6 Chain Rule
2.7 Implicit Differentiation
2.8 Derivatives of Exponential Functions
2.9 Derivatives of Logarithmic Functions
2.10 Logarithmic Differentiation
2.11 Derivatives of Inverse Trig Functions
Unit 3 Differentiation Theorems 2 weeks – September
3.1 Intermediate Value Theorem
3.2 L'Hospital's Rule
3.3 Sketching Derivatives
3.4 Maximum & Minimum Values
3.5 The Mean Value Theorem
3.6 First Derivatives Test
3.7 Second Derivatives Test
3.1 Intermediate Value Theorem
3.2 L'Hospital's Rule
3.3 Sketching Derivatives
3.4 Maximum & Minimum Values
3.5 The Mean Value Theorem
3.6 First Derivatives Test
3.7 Second Derivatives Test
Units 4 Integration Concepts & Techniques 3.5 weeks - October
4.1 Antiderivatives introduction to indefinite integrals
4.2 Area & Distances including Trapezoidal & Midpoint Rules
4.3 The Fundamental Theorem of Calculus Introduction to Definite Integrals
4.4 Substitution Rule for Integration
4.5 Substitution Rule for Integration involving Trigonometric Identities
4.6 Integration by Parts
4.7 Partial Fraction Integration
4.8 Improper Integrals
Units 5 Differentiation & Integration Applications 3 weeks - Ending October/Beginning November
5.1 Average Value of Function
5.2 Areas between Curves
5.3 Volumes of solids of revolution Shell Method
5.4 Volumes of solids of revolution Disk Method
5.5 Optimization
5.6 Related Rates
5.7 Slope Fields with Euler's method
5.8 The Logistical Curve
4.1 Antiderivatives introduction to indefinite integrals
4.2 Area & Distances including Trapezoidal & Midpoint Rules
4.3 The Fundamental Theorem of Calculus Introduction to Definite Integrals
4.4 Substitution Rule for Integration
4.5 Substitution Rule for Integration involving Trigonometric Identities
4.6 Integration by Parts
4.7 Partial Fraction Integration
4.8 Improper Integrals
Units 5 Differentiation & Integration Applications 3 weeks - Ending October/Beginning November
5.1 Average Value of Function
5.2 Areas between Curves
5.3 Volumes of solids of revolution Shell Method
5.4 Volumes of solids of revolution Disk Method
5.5 Optimization
5.6 Related Rates
5.7 Slope Fields with Euler's method
5.8 The Logistical Curve
SPRING SEMESTER - BC TOPICS
Unit 6 Sequences & Series 5 Weeks January/Beginning February
6.1 Introduction to Sequences
6.2 Introduction to Series
6.3 The Integral Test
6.4 The Comparison Test
6.5 Alternating Series Test
6.6 Absolute Convergence and The Ratio and Root Tests
6.7 Power Series
6.8 Representations of Functions as Power Series
6.9 Taylor Series/Maclaurin Series
6.10 Applications of Taylor Polynomials
Unit 7 Parametric & Polar Functions 4 Weeks February
7.1 Introduction to Parametric Curves
7.2 Tangents & Areas involving Parametric Curves
7.3 Arc Length & Surface Area involving Parametric Curves
7.4 Introduction to Polar Coordinates
7.5 Areas & Lengths in Polar Coordinates
7.6 Vector Calculus
6.1 Introduction to Sequences
6.2 Introduction to Series
6.3 The Integral Test
6.4 The Comparison Test
6.5 Alternating Series Test
6.6 Absolute Convergence and The Ratio and Root Tests
6.7 Power Series
6.8 Representations of Functions as Power Series
6.9 Taylor Series/Maclaurin Series
6.10 Applications of Taylor Polynomials
Unit 7 Parametric & Polar Functions 4 Weeks February
7.1 Introduction to Parametric Curves
7.2 Tangents & Areas involving Parametric Curves
7.3 Arc Length & Surface Area involving Parametric Curves
7.4 Introduction to Polar Coordinates
7.5 Areas & Lengths in Polar Coordinates
7.6 Vector Calculus